I personally don't know any traditional archer wearing a chest protector. I noticed however that Olympic archers (and similar disciplines) nearly always wear one. Which circumstances should make me think about wearing such?
Chest guards works as the same of arm guards. It protects the archer from get the sting from the string.
Although, when an archer shoots his/her arm, it's more likely it's related to his/her form while shooting his/her chest is a natural body shape fact. (not an actual problem, just as it is.)
It's also very commonly used by girls for obvious reason but some guys with a slightly longer draw length might use it as well.
There doesn't seem to be anything in the (UK) rules saying this is required (unlike shooting jackets)
Protective accessories may be used such as finger-protective tape or gloves, chest protectors, and arm guards
As I understand it the chest protector is simply to allow you to pull the draw very close to your chest without it rubbing and hurting (and to prevent it getting caught on something)
So my guess is simply for protection. If you shoot enough arrows in a day (Olympic standard achers are going to practice a lot!) then I guess it's easy for your chest to get sore.